Investigation of the parameters affecting the behavior of RC beams strengthened with FRP

Abstract

Three-point bending tests were carried out on nineteen Reinforced Concrete (RC) beams strengthened with FRP in the form of completely wrapping. The strip width to spacing ratios, FRP type, shear span to effective depth ratios, the number of FRP layers in shear, and the effect of stirrups spacing were the parameters investigated in the experimental study. The FRP contribution to strength on beams having the same strip width to spacing ratios could be affected by the shear span to effective depth ratios and stirrups spacing. The FRP contributions to strength were less on beams with stirrups in comparison to the tested beams without stirrups. Strengthening RC beams using FRP could change the failure modes of the beams compared to the reference beam. In addition to the experimental study, a number of equations used to predict the FRP contribution to the shear strength of the strengthened RC beams were assessed by using a limited number of beams available in the literature. The effective FRP strain is predicted by using test results, and this prediction is used to calculate the FRP contribution to shear strength in ACI 440.2R (2017) equation. Based on the statistical values of the data, the proposed equation has the lowest coefficient of variation (COV) value than the other equations.

Graphical abstract

Keywords

carbon / glass / strengthening / shear strength / reinforced concrete beam / fiber reinforced polymer

1 Introduction

Fiber-reinforced polymer (FRP) is a composite material that can be used to strengthen deteriorated reinforced concrete (RC) elements due to its superior properties such as high strength to weight ratio, easy to install, corrosion resistance, etc. FRP can be used to increase the axial compressive strength of RC columns by confining effect and in flexural and shear strengthening of RC elements. The performance of FRP-strengthened elements and the parameters affecting behavior have been examined in many studies. These studies have contributed significantly to the understanding of the behavior of FRP-strengthened elements. The performance of FRP-strengthened beams and the parameters affecting the behavior of the strengthened beams have been experimentally investigated by various researchers [1–59]. Some researchers [48–64] conducted analytical studies and proposed equations for the calculation of the contribution of FRP to shear strength using an effective strain developed along FRP. Triantafillou [49] stated there is an inverse relationship between effective strain and axial rigidity of FRP sheet and the value of effective strain decreases as the value of axial rigidity increases.

Ozbakkaloglu et al. [65] have written a detailed review article to investigate the performance of the proposed stress-strain models of FRP-confined concrete under axial compression. Naser et al. [66] have proposed strategies to perform finite element simulations on FRP-strengthened structures and have given methods to simulate materials, adhesives, etc. Statistical assessment of the proposed equations for the calculation of the FRP contribution to shear strength has been performed by Lima and Barros [67], Pellegrino and Vasic [68], and Kotynia et al. [69]. Some researchers [30,33,36,44] have tested RC beams by strengthening in both shear and flexure with the FRP and assessing the performance and behavior of the elements. It has been stated by Chen and Teng [60] that the RC beams strengthened with FRP in shear are failed in two different ways, usually FRP rupture and FRP debonding, and this depends on the form of strengthening with FRP. FRP rupture generally occurs on completely wrapped beams with FRP. FRP debonding is a major problem that usually occurs in side-bonded and U-wrapped beams with FRP. The debonding failure of FRP reduces FRP contribution to strength and efficiency in behavior. Detailed information about FRP debonding can be found in the study of Kang et al. [70]. The near-surface mounted (NSM) [71–77] and grooving methods (GM) [27,30,72,78] have been proposed as alternatives to externally bonded FRP (EBR) in order to delay the peeling of FRP from the concrete surface. It can be concluded that NSM and GM are more effective than EBR in delaying FRP debonding and also provide significant contributions to shear strength.

The effect of stirrups [1,5,6,8,9,15,17,18,22–24,31,32,40,50–54,56], the shear span to effective depth ratios (a/d) [6,10,16–19,22,25,36,43,53,54], size effect [5,9,20,21,28,79], and the effect of shear strip width to spacing ratio (w_f/s_f) [10,29,32,40] on the behavior of RC beams strengthened with FRP have been investigated experimentally and analytically. It has been demonstrated in the studies carried out by Bousselham and Chaallal [5], Pellegrino and Modena [50], and Khalifa and Nanni [53] that the stirrups ratio (ρ_w) is an important parameter affecting the performance and FRP contribution on the strengthened beams. Researchers [5,50,53] stated that there may be a potential interaction between FRP and stirrups, which can negatively affect each other’s contributions to shear strength. a/d is another parameter that has significant effects on the performance and behavior of beams strengthened with FRP as stated by Li and Leung [16], Khalifa et al. [18], Guadagnini et al. [43], and Cao et al. [54]. Hence, this parameter should be taken into account when calculating the contribution of FRP. Therefore, the authors have aimed to examine the effect of FRP type (C, and G), different stirrups spacing (s), w_f/s_f, a/d, and the number of FRP layers in shear experimentally. In addition to the experimental study, a number of equations for predicting the contribution of FRP to the shear strength of strengthened RC beams were assessed by using a limited number of beams available in the literature.

2 Experimental program

RC beams with three different a/d (2.5, 3.5, and 4.5), and two different stirrups spacing (s), were tested with a three-point bending test. The beams were strengthened and tested using two different types of CFRP or GFRP with completely wrapping technique.

2.1 Properties of the strengthened beams

The dimensions and strengthening configurations of the tested beams were shown schematically in Fig.1. The beams were divided into four series according to the s and a/d, and one beam in each series was tested as a reference beam without being strengthened. The other beams in each series were strengthened and tested with GFRP or CFRP in both shear and flexure. Completely wrapped discrete FRP strips were applied to strengthen the beams in shear, at an angle of 90° to the beam axis. The flexural strengthening was carried out by bonding two layers of FRP with a width of 150 mm to the soffit of the beam. The strengthening details such as the FRP type (CFRP/GFRP), the number of FRP layers (n_s) and widths of FRP strips (w_f) used in shear, the net distance between two adjacent strips (s_n), the total length of the beam (l), the length of beams between supports (l_n), the spacing of the stirrups (s), distance from the center to the center of the two FRP strips side by side (s_f), the number of FRP layers applied for flexural strengthening (n_f), w_f/s_f and total FRP reinforcement ratios (ρ_f) applied for shear reinforcement were given in Tab.1.

Each specimen was designated by using distinctive notations as given in Tab.1 where “2.5, 3.5, and 4.5” refer to the a/d, “C (CFRP)” and “G (GFRP)” refers to the type of FRP, “S20” refers to the distance of the stirrups on beams with stirrups (unit: cm), “S0” indicates the beams without stirrups, “5/10” is the clear distance (unit: cm) between two neighboring FRP strips and “2K” refers to the using of two layers of FRP in shear.

2.2 Materials

Ready-mixed concrete supplied by a local concrete company was preferred to manufacture the beams to be tested. In order to determine the compressive strength of the concrete, nine concrete cube samples (150 mm × 150 mm × 150 mm) were taken during concrete casting. In order to obtain the compressive strength of concrete, compression tests were carried out on cube samples. The compressive strength of concrete was found to be 43 MPa. In all series, two rebars with a diameter of 18 mm (2Ø18) formed the tension reinforcement at the bottom of the beams. The yield strength, ultimate strength, and modulus of elasticity of the tension reinforcements were 502 MPa, 654 MPa, and 200 GPa, respectively. The compression reinforcements comprising of two rebars with a diameter of 12 mm (2Ø12) were used at the top of the beam in K2.5S20 and K3.5S20 series. The mechanical properties of the compression reinforcements (2Ø12) were obtained as follows: Elasticity modulus of 200 GPa, the yield strength of 506 MPa, and the ultimate strength of 662 MPa. In the K2.5S20 and K3.5S20 series, stirrups with a diameter of 8 mm (Ø8) placed with an interval of 200 mm along the beam were used. The steel stirrups (Ø8) had a yield strength of 610 MPa, the ultimate strength of 788 MPa, and an elasticity modulus of 200 GPa. Epoxy, which consisted by mixing the resin and hardener in certain proportions proposed by the manufacturer, was used to bond the FRP to the concrete surface of the beams. The mechanical properties of CFRP given by the manufacturer were as follows: modulus of elasticity of 255 GPa, the tensile strength of 4400 MPa. The manufacturer gave the mechanical properties of GFRP as follows: modulus of elasticity of 73 GPa, the tensile strength of 3300 MPa. The design thicknesses of CFRP and GFRP are 0.34 and 0.36 mm, respectively.

2.3 Loading and test setup

The beams were tested under a static rate (30 μ/s) of concentrated loading at mid-span using a displacement-controlled loading machine. The experimental data such as deflections, strains, and loads were recorded by the computer-aided data acquisition system. The vertical deflection occurring at the mid-span of the beam during the experiment was measured and recorded using linear variable displacement transducers (LVDTs) as shown in Fig.1. In the experiment, strain gauges were used to measure the strains occurring in the longitudinal reinforcement and stirrups. The strains occurring in the stirrups in K2.5S20 and K3.5S20 series were measured using two strain gauges placed taking into consideration the possible shear crack (Fig.1). In the K2.5S20 series, strain gauges were attached to both arms of the third stirrups. In the K3.5S20 series, strain gauges were attached to the third and fourth stirrups. In all elements, one strain gauge was also attached to the determined points on the longitudinal reinforcement (Fig.1).

3 Test results and discussion

The general behavior of the tested elements was evaluated in terms of strength, ductility, stiffness, failure modes, and strains by using the load-deflection and strain-deflection curves. Then, the parameters such as a/d, and the effect of stirrups were examined separately.

3.1 The main results obtained in the tested beams

3.1.1 Strength, ductility, and stiffness

Considering the test results, the strengthening with CFRP/GFRP enhances the load-carrying and deflection capacities compared to the reference beams in each series as seen in Fig.2(a) and 2(b). In K2.5S20 and K3.5S0 series, the increase in load carrying, deflection capacities, and the contribution of FRP to strength is higher in CFRP than GFRP-strengthened beams since CFRP has better mechanical properties. In all series, as decreasing w_f/s_f, CFRP/GFRP contribution to strength and the load-carrying capacity decreases in the strengthened beams having the same number of FRP layers on account of a decrease in the number of FRP shear strips intersected with the diagonal cracks. Even though strengthening the RC beams with a single layer of CFRP was more effective in order to develop the load-carrying capacities of beams in the K4.5S0 series, (Tab.2). In the K2.5S20 series, increasing the number of FRP layers from one to two improves the load-carrying capacities and CFRP contribution to strength. In the K2.5S20 and K4.5S0 series, the addition of a second layer of CFRP in shear limits the progression and expansion of cracks as seen in Fig.3, further increasing the ductility indexes, the area under the load-deflection curves, and the deflection capacities RC beams. In K3.5S20, K4.5S0, and K2.5S20 series, decreasing the w_f/s_f induces an increment in the ductility capacities of the CFRP strengthened beams contrary to the K3.5S0 series. Hence, it can be concluded that the number of FRP layers used for shear strengthening, FRP type (CFRP/GFRP), and w_f/s_f affect the load-carrying, deflection, and ductility capacities of the tested beams with FRP.

In all series, the increase in the initial stiffness of the FRP strengthened beams varies between 8%–56%. In the K2.5S20 series, the increase in the initial stiffness of GFRP strengthened beam was more than the beams with CFRP contrary to the K3.5S0 series. In K2.5S20, K3.5S20, and K4.5S0 series, the increase in the initial stiffness of the RC beams having the same number of FRP layers becomes lower as the w_f/s_f decreases, since the distance between the shear strips of FRP increases, the crack limitation by FRP and confinement effect of FRP on beam decreases.

3.1.2 Failure modes and cracking structures

The failure modes of the reference beams (K2.5S20-R, K3.5S0-R, K3.5S20-R, and K4.5S0-R) were shear failure occurring suddenly as a result of the diagonal shear crack starting over the supports and extending to the load application point as shown in Fig.4. There were no obvious flexural cracks in the middle span of the reference beams during the experiment.

There was a shear failure caused by the rupture of the FRP shear strips which intersects with shear cracks in the shear spans of the beams (K2.5S20-G-5, K2.5S20-G-10, K2.5S20-C-10-2K, K3.5S0-G-5, K3.5S0-C-10, K3.5S0-G-10, K3.5S20-C-10, and K4.5S0-C-10-2K) as seen in Fig.4. The shear cracks in the beams strengthened with GFRP were wider than CFRP since GFRP had lower mechanical properties. Thus, it can be observed that the FRP type changes the crack width and pattern of the tested beams.

The crushing of the concrete as a result of increased compressive stresses under the load application point induced the element K3.5S0-C-5 to fail in flexure. K2.5S20-C-5, K2.5S20-C-10, K3.5S0-C-5, K3.520-C-5, K4.5S0-C-5, and K4.5S0-C-10 failed as a result of a rupture in the FRP, which was attached to the tension face of the beam to increase the flexural strength (Fig.4). According to the test results, it was observed that the number of FRP layers used in shear, a/d, and the w_f/s_f have a significant effect on the modes of failure and crack structures of the beams. The shear cracks become pronounced, as w_f/s_f decreases. K4.5S0-C-5-2K failed with fracture of the CFRP shear strips due to the flexural and diagonal tension cracks that occurred at the mid-span of the beam. In addition, the flexural effect in the behavior and failure modes of the beams with FRP become more obvious with increasing in a/d.

3.1.3 Longitudinal reinforcement strains

The longitudinal reinforcement yielded on all beams in the K2.5S20, K3.5S0, and K3.5S20 series except for K2.5S20-C-5, K3.5S0-R, and K3.5S0-C-10 beams before the failure occurred as seen in the strain-deflection curves (Fig.5). The strain-deflection curves for the longitudinal reinforcement of all beams were given as ε₁ in Fig.5. The maximum-recorded strains on the longitudinal reinforcement were generally higher in the beams strengthened with FRP than the reference beams K2.5S20-R, K3.5S0-R, and K3.5S20-R except for K2.5S20-C-5 and K3.5S0-C-10 due to increment in the load-carrying and deflection capacities of the strengthened beams. Unlike the K2.5S20, K3.5S0, and K3.5S20 series, strengthening with CFRP reduces the maximum strain value measured in longitudinal reinforcements in K4.5S0 series except for K4.5S0-C-5-2K compared to the reference beam (K4.5S0-R). Increasing the number of FRP layers in shear enlarged the cross-sectional area carrying the bending moment at the soffit of the beams and resulted in a decrease in the strains occurring in the longitudinal reinforcement at the same load values. However, the increase in the number of FRP layers used in shear develops the maximum strain value in the longitudinal reinforcement.

The strain on longitudinal reinforcement of K2.5S20, K3.5S20, and K4.5S0 series strengthened with single-layer CFRP in shear increases as the w_f/s_f decrease contrary to the K3.5S0 series. In the strengthened beam, the strain values measured in the longitudinal reinforcements at the same load levels were less in comparison to reference beams due to the flexural strengthening at the bottom of the beam. The strain values on the longitudinal reinforcements of the tested beams having the same w_f/s_f were bigger on GFRP strengthened beams than beams with CFRP at the same load levels in K3.5S0 and K2.5S20 series beams since GFRP has a lower modulus of elasticity and tensile strength. Hence, it might be assessed that the strain behavior of the longitudinal reinforcement is affected by the w_f/s_f and the FRP type.

3.1.4 Stirrups strains

The strain gauges were placed on both hands of the third stirrups (S2 and S3) in the K2.5S20 series and the fourth (S2) and third stirrups (S3) in the K3.5S20 series as shown in Fig.1. The strain-deflection curves for all series and the strain values of S2 and S3 were given as ε₂ and ε₃ in Fig.5, respectively. The horizontal lines ε_y,tensile and ε_y,stirrups determine the yielding strains of both longitudinal and stirrups, respectively (Fig.5).

It is shown that the stirrups on K2.5S20-R and K3.5S20-R beams did not yield before the failure occurred experimentally. The stirrups yielded on strengthened beams in K2.5S20 series (Fig.5). It could be evaluated by considering the test results; using FRP increases the maximum recorded stirrups strain on the tested beams in comparison to the K2.5S20-R by changing the cracking patterns and increasing the strength of beams. Contrary to GFRP strengthened beams, the strain values recorded on the beams with CFRP were lower than the reference beam at the same load levels. In beams with the same number of FRP layers in shear, increasing the distance between the FRP shear strips (w_f/s_f) enhances the strain values on both GFRP and CFRP strengthened beams in the K2.5S20 series. In addition, increasing the number of CFRP layers applied in shear strengthening mitigates the strain values of stirrups at the same load levels compared to beams having single layer CFRP due to the higher efficiency in limiting the width of the diagonal shear crack. Provided that the beams have the same w_f/s_f, GFRP strengthened beams have higher strain values than beams with CFRP at the same load levels.

The strain values of S2 and S3 in the K3.5S20 series were given as ε₂ and ε₃ in Fig.5, respectively. The test results showed these results. Strengthening RC beams with CFRP improves the strain values of both the third (ε₃) and fourth stirrups (ε₂) compared to K3.5S20-R. The third and fourth stirrups on K3.5S20-C-5 yielded before the failure occurred. However, the third stirrup yielded; the fourth stirrup did not yield on K3.5S20-C-10. Since the strains in the stirrups were very small at low load values, the stirrups in the tested beams do not contribute much to the strength. After the first diagonal shear cracks formed, the stirrups in the beams began to deform more and contribute to the shear strength. Because the diagonal shear crack intersected the third stirrups previously, the third stirrups started to take the load actively earlier than the fourth stirrups. Since the shear cracks in the region of the third stirrup were wider, the third stirrup had higher strain values than the fourth stirrup. As the w_f/s_f decrease, the maximum strains of the third stirrup on the strengthened beams increases. Furthermore, the stirrup strains recorded on the strengthened beams were lower than the reference beams at the same load levels.

3.2 Parameters affecting the performance of RC beams with FRP strengthening

3.2.1 Shear span to effective depth ratios (a/d)

It can be seen that as the a/d increased, there was a decrease in the initial stiffness of the reference beams and an increase in the number of prominent cracks. Therefore, deflection capacities (Fig.2(b)), ductility capacities (Fig.3), the maximum strains on longitudinal reinforcement (Fig.5), and stirrups (Fig.5) of reference beams (K2.5S20-R, K3.5S0-R, K3.5S20-R, and K4.5S0-R) enhance for beams with/without stirrups based on test results.

The load-carrying capacities of strengthened (K3.5S0-C-5, K4.5S0-C-5, K3.5S20-C-5, K2.5S20-C-5, K4.5S0-C-10, K3.5S0-C-10, K2.5S20-C-10, and K3.5S20-C-10) beams become lower as the a/d increased as noticed in Fig.3. FRP contributions to strength were not the same for beams. As the a/d increased, the FRP contributions to strength were higher on beams without stirrups (K3.5S0-C-5, K4.5S0-C-5, K3.5S0-C-10, K4.5S0-C-10). However, the FRP contributions to strength were smaller on beams with stirrups (K2.5S20-C-5, K3.5S20-C-5, K2.5S20-C-10, K3.5S20-C-10). The reason could be explained as the a/d increases, tensile stresses consisting of flexural behavior in the beams with stirrups become more prominent and cracks are concentrated mainly in the middle of the beam. The number of diagonal cracks and FRP shears strips intersecting with diagonal cracks decreases. Hence, the contribution of FRP to strength and the stirrups strains decreases as the a/d ratio increases.

It is observed that a/d affects the deformation in the longitudinal reinforcement and deflection capacities in different ways depending on whether it is with or without stirrups since a/d and stirrups affect the cracking pattern, location of the prominent cracks, and failure modes by changing the flexural behavior of the tested beams. Also, the increase in the initial stiffness of these beams according to the reference beams depended on the a/d. The ductility capacities of, K3.5S0-C-10, K2.5S20-C-10, K4.5S0-C-10, and K3.5S20-C-10 beams improve for beams with/without stirrups as the a/d increase contrary to the beams K3.5S0-C-5, K2.5S20-C-5, K4.5S0-C-5, and K3.5S20-C-5.

Based on experimental results, the a/d affects the performance, deflection capacities, ductility capacities, and the behavior of the reference and strengthened beams having the same w_f/s_f. The strain recorded on stirrups was affected by the a/d. Therefore, the effect of a/d, which is an important parameter, should be taken into account when calculating the contribution to strength by FRP.

3.2.2 The influence of stirrups

Considering the K3.5S0-C-5, K3.5S20-C-5, K3.5S0-C-10, and K3.5S20-C-10 beam with the same a/d and w_f/s_f, the load-carrying capacities become higher on beams with stirrups compared to beams without stirrups due to the contribution of stirrups to strength.

In beams without stirrups, only FRP shear strips carry the shear force after the diagonal shear cracks occurred, while in elements with stirrups, the shear force is carried by both the transverse reinforcement and the FRP. Therefore, the FRP contributions to strength were less on beams with stirrups in comparison to the beams without stirrups. Since the stirrups limit the width of the shear cracks; slow its progress and expansion, the deflection capacities, the ductility capacities, and the increase in the initial stiffness were higher for beams with stirrups compared to beams without stirrups. The effect of stirrups on the behavior and the FRP contribution to strength should be considered in calculating the FRP contribution. However, this effect is not considered in predictions equations (Triantafillou [49], Khalifa and Nanni [53], Khalifa et al. [62], ACI 440.2R (2017) [80], Fib-TG 9.3 (2001) [81]) used for FRP contributions.

4 Analytical study

The accuracy of Triantafillou [49], Khalifa and Nanni [53], Khalifa et al. [62], ACI 440.2R (2017) [80], Fib-TG 9.3 (2001) [81] was evaluated separately using the data collected from the literature. A total of 81 FRP strengthened specimens in the form of completely wrapping in shear were examined (Leung et al. [28], Diagana et al. [29], Ianniruberto and Imbimbo [58], Cao et al. [54], Guadagnini et al. [43], Grande et al. [1], Bukhari et al. [55], Saafan [44], Li and Leung [16], Araki et al. [82], Zhao and Xie [83], Miyajima et al. [84], Teng et al. [15], Mostofinejad et al. [27], Uji [85], Funakawa et al. [86], Umezu et al. [87]). Collected data contains three various types of FRP (Carbon: C; Glass: G and Aramid: A). The number of GFRP, AFRP, and CFRP strengthened beams were 14, 3, and 64, respectively. The ratios of the experimental (V_exp) to predicted FRP contribution (V_frp) were evaluated using the coefficient of variation (COV), standard deviation (SD), and mean value (MV) calculated for each of the equations. The calculated values of MV, SD, and COV were given in Tab.3.

The effective strain values of two completely wrapped beams of the collected data could not be calculated because the equation proposed by Khalifa and Nanni [53] could not be applied in cases where axial rigidity (ρ_fE_f) was greater than 0.7 GPa. According to the results given in Tab.3, all equations give conservative MVs and demonstrate a considerable dispersion with the COV ranging from 0.684 to 0.903. The ACI 440.2R prediction has the highest MV and COV, hence it gives the most conservative results than the other equations taken into account. The authors believe that the design value of 0.004 given for effective FRP strain in ACI 440.2R causes the most conservative results compared to other equations. The equation given by Khalifa et al. [62] shows conservative results and has lower COV values compared to Fib-TG 9.3 and ACI 440.2R. Since Triantafillou [49] and Khalifa et al. [62] have the lowest COV values for beams collected from literature compared to the other equations, Triantafillou [49] and Khalifa et al. [62] give more reliable results. Taking into account equations except ACI 440.2R gives the effective FRP strain based on axial rigidity. Therefore, they give more reliable results compared to ACI 440.2R (2017).

The effectiveness of strengthening RC beams with FRP and the contribution of FRP to shear strength depends on the effective strain occurring along with FRP sheets and the axial rigidity of FRP. As the FRP strips or sheets become stiffer and thicker, debonding of FRP becomes more important than tensile fracture, and the effective FRP strain reduced in especially side bonded and U-wrapped beams as expressed by Triantafillou [49]. Triantafillou stated that effective strain is not constant, but decreases as the FRP axial rigidity increases. In addition, FRP contribution to shear strength increases almost linearly with axial rigidity up to approximately 0.4 GPa, beyond which the effectiveness of FRP is minimal. Therefore, Triantafillou [49] and Khalifa and Nanni [53] noted that there is an optimum amount of FRP and that the strengthening effect does not change much in cases above this limit value. This conclusion is particularly useful in designing FRP reinforcements and determining optimum material quantities. Based on test data in this study, it is seen that there is an inverse relationship between axial rigidity and effective FRP strain (Fig.6). Hence, it may not suitable to give a constant value for the calculation of the effective FRP strain as in ACI 440.2R. For this reason, its use was investigated by not taking a constant value for the effective FRP strain in the equation suggested by ACI 440.2R (2017). An equation to calculate the effective FRP strain is given by using the RC beams failing in shear based on the experimental results of this study, using two parameters. These parameters are theoretical effective strain (ε_frp,e) and axial rigidity (ρ_fE_f). The ε_frp,e is obtained using the equation given in ACI 440.2R to calculate the shear contribution of FRP and the experimental FRP contribution to shear strength (V_frp). The FRP contribution to shear strength, the ε_frp,e, and ρ_fE_f of beams are given in Tab.4 and Fig.6, experimentally. The best-fit equation obtained from these data to calculate the ε_frp,e was given below in Eq. (1), and ε_frp,e decreases as ρ_fE_f increases as shown in Fig.6.

(1){\epsilon }_{\mathrm{f}\mathrm{e}}=0.0018{\left({\rho }_{\mathrm{f}}{E}_{\mathrm{f}}\right)}^{-0.84}.

The FRP contributions to shear strength were calculated using Eq. (1) in the ACI prediction equation, therefore the ACI prediction was modified and this modified ACI prediction was evaluated in the literature and these beams of the study. Based on the statistical values of the data in Tab.3, the proposed equation has the lowest COV value than the other equations. Therefore, it could be used to calculate the FRP contributions for beams strengthened with FRP in the form of completely wrapping.

The effective strain values calculated using Eq. (1) were compared with the experimentally measured strains using collected data from the literature to examine the validity of the proposed equation in the calculation of effective strain. The experimentally and predicted effective strain values calculated using different equations were given in Tab.5. The ratios of the experimental strain (ε_exp) to predicted effective strains (ε_pre) calculated by equations were evaluated using the MV, SD, and COV calculated for each of the equations given in Tab.6. When statistical results are evaluated (Tab.6), it is seen that the proposed equation can be used in the calculation of effective strain.

5 Conclusions

The main and important findings obtained in the experimental and analytical study are presented below.

1) Strengthening RC beams in both flexure and shear with GFRP/CFRP has enhanced the load-carrying and deflection capacities in comparison to the reference specimens. In K2.5S20 and K3.5S0 series, the shear contribution of FRP and the increase in the load-carrying, deflection capacities are greater in CFRP strengthened beams than the beams strengthened with GFRP as a result of the better mechanical properties of CFRP.

2) The w_f/s_f and FRP types have a significant effect on the deflection, load-carrying, and ductility capacities of the strengthened beams.

3) Since the shear cracks occurring on the GFRP strengthened beams are wider than the CFRP strengthened beams, it can be said that FRP type affects the cracking structures and crack width occurring in beams. In addition, the results of the experiment showed that strengthening with FRP in both shear and flexure changed the cracking pattern and failure modes of the beams in comparison to unstrengthened reference beams.

4) Using FRP increases the maximum recorded stirrups strain on the strengthened beams in comparison to reference specimens in the ultimate state. The measured strains of the beams with CFRP were lower than the reference beam at the same load levels, contrary to GFRP strengthened beams.

5) In beams with the same number of FRP layers in shear, decreasing the w_f/s_f by increasing the distance between the FRP shear strips enhances the strain values of stirrups at the same load levels on both GFRP and CFRP strengthened beams. Besides, increasing the number of CFRP layers, the strain values of stirrups decrease at the same load levels compared to beams having single layer CFRP.

6) The load-carrying capacities of strengthened beams become lower as the a/d increase. As the a/d increased, the FRP contributions to strength were higher on beams without stirrups. However, the FRP contributions to strength were smaller on beams with stirrups. The strain recorded on stirrups was affected by the a/d. Therefore, this parameter should be taken into account when calculating the contribution of FRP.

7) The FRP contributions to strength were less on beams with stirrups in comparison to the beams without stirrups. The effect of stirrups on the behavior and the FRP contribution to strength should be considered in calculating the FRP contribution.

8) Based on test data in this study, it is seen that there is an inverse relationship between axial rigidity and effective FRP strain. Hence, it may not suitable to give a constant value for the calculation of the effective FRP strain

9) In ACI 440.2R (2017), FRP effective strain is taken as a constant limit value to predict the FRP contribution to shear strength, however, it can be seen an inverse relationship between axial rigidity and effective FRP strain based on the test results. The effective FRP strain is predicted by using the proposed equation, and this prediction is used to calculate the FRP contribution to shear strength in ACI 440.2R equation. Based on the statistical values of the data, the proposed equation has the lowest COV value than the other equations. Therefore, it could be used to calculate the FRP contributions for the strengthened beams with FRP in the form of completely wrapping.

References

[1] GrandeE, ImbimboM, RasuloA. Effect of Transverse steel on the response of RC Beams strengthened in shear by FRP: Experimental study. Journal of Composites for Construction, 2009, 13( 5): 405– 414

[2] LeeH K, CheongS H, HaS K, LeeC G. Behavior and performance of RC T-section deep beams externally strengthened in shear with CFRP sheets. Composite Structures, 2011, 93( 2): 911– 922

[3] KimG, Sim J, OhH. Shear strength of strengthened RC beams with FRPs in shear. Construction & Building Materials, 2008, 22( 6): 1261– 1270

[4] DamnooD J, KumarS. Experimental study on post repair performance of reinforced concrete beams rehabilitated and strengthened with CFRP sheets. Research Journal of Engineering and Technology, 2016, 7( 3): 103– 114

[5] BousselhamA, ChaallalO. Mechanisms of shear resistance of concrete beams strengthened in shear with externally bonded FRP. Journal of Composites for Construction, 2008, 12( 5): 499– 512

[6] BousselhamA, ChaallalO. Effect of transverse steel and shear span on the performance of RC beams strengthened in shear with CFRP. Composites Part B: Engineering, 2006, 37( 1): 37– 46

[7] BencardinoF, SpadeaG, SwamyR N. The problem of shear in RC beams strengthened with CFRP laminates. Construction & Building Materials, 2007, 21( 11): 1997– 2006

[8] AbassA L, HassanY R. Shear behavior of reinforced concrete wide beams strengthened with CFRP sheet without stirrups. Diyala Journal of Engineering Sciences, 2019, 12( 1): 80– 98

[9] BenzeguirZ E A El-SaikalyG ChaallalO. Influence of size on the behavior of RC T-beams strengthened in shear with externally bonded CFRP. In: 9th International Conference on Fibre-Reinforced Polymer (FRP) Composites in Civil Engineering (CICE 2018). Paris: IIFC, 2018, 750– 755

[10] JayaprakashJ, Abdul SamadA A, Anvar AbbasovichA, Abang AliA A. Shear capacity of precracked and non-precracked reinforced concrete shear beams with externally bonded bi-directional CFRP strips. Construction & Building Materials, 2008, 22( 6): 1148– 1165

[11] GalalK, MofidiA. Shear strengthening of RC T-beams using mechanically anchored unbonded dry carbon fiber sheets. Journal of Performance of Constructed Facilities, 2010, 24( 1): 31– 39

[12] CarolinA, TäljstenB. Experimental study of strengthening for increased shear bearing capacity. Journal of Composites for Construction, 2005, 9( 6): 488– 496

[13] ChaallalO, NolletM J, PerratonD. Shear strengthening of RC beams by externally bonded side CFRP strips. Journal of Composites for Construction, 1998, 2( 2): 111– 113

[14] HaddadR H, MarjiC S. Composite strips with U-shaped CFRP wrap anchor systems for strengthening reinforced concrete beams. International Journal of Civil Engineering, 2019, 17( 11): 1799– 1811

[15] TengJ G, ChenG M, ChenJ F, RosenboomO A, LamL. Behavior of RC beams shear strengthened with bonded or unbonded FRP wraps. Journal of Composites for Construction, 2009, 13( 5): 394– 404

[16] LiW, Leung C K Y. Shear span–depth ratio effect on behavior of RC beam shear strengthened with full-wrapping FRP strip. Journal of Composites for Construction, 2016, 20( 3): 04015067

[17] BousselhamA, ChaallalO. Behavior of reinforced concrete T-beams strengthened in shear with carbon fiber-reinforced polymer-an experimental study. ACI Structural Journal, 2006, 103( 3): 339– 347

[18] KhalifaA BelarbiA NanniA. Shear performance of RC members strengthened with externally bonded FRP wraps. In: Proceedings of Twelfth World Conference on Earthquake, Auckland: Upper Hutt, N.Z., 2000

[19] LiW, Leung C K Y. Effect of shear span-depth ratio on mechanical performance of RC beams strengthened in shear with U-wrapping FRP strips. Composite Structures, 2017, 177 : 141– 157

[20] BenzeguirZ E A, El-SaikalyG, ChaallalO. Size effect in RC T-beams strengthened in shear with externally bonded CFRP sheets: Experimental study. Journal of Composites for Construction, 2019, 23( 6): 04019048

[21] BenzeguirZ E A, El-SaikalyG, ChaallalO. Size effect of RC T-beams strengthened in shear with externally bonded CFRP L-shaped laminates. Journal of Composites for Construction, 2020, 24( 4): 04020031

[22] LiA, Diagana C, DelmasY. CRFP contribution to shear capacity of strengthened RC beams. Engineering Structures, 2001, 23( 10): 1212– 1220

[23] LiA, Diagana C, DelmasY. Shear strengthening effect by bonded composite fabrics on RC beams. Composites Part B: Engineering, 2002, 33( 3): 225– 239

[24] KhalifaA, TumialanG, NanniA, BelarbiA. Shear strengthening of continuous RC beams using externally bonded CFRP sheets. In: Proceedings of 4th International Symposium on FRP for Reinforcement of Concrete Structures (FRPRCS4). Baltimore: American Concrete Institute, 1999, 995– 1008

[25] AllamS M, EbeidoT I. Retrofitting of RC beams predamaged in shear using CFRP sheets. Alexandria Engineering Journal, 2003, 42( 1): 87– 101

[26] AdhikaryB B, MutsuyoshiH. Behavior of concrete beams strengthened in shear with carbon-fiber sheets. Journal of Composites for Construction, 2004, 8( 3): 258– 264

[27] MostofinejadD, HosseiniS A, RazaviS B. Influence of different bonding and wrapping techniques on performance of beams strengthened in shear using CFRP reinforcement. Construction & Building Materials, 2016, 116 : 310– 320

[28] LeungC K Y, ChenZ, LeeS, Ng M, XuM, TangJ. Effect of size on the failure of geometrically similar concrete beams strengthened in shear with FRP strips. Journal of Composites for Construction, 2007, 11( 5): 487– 496

[29] DiaganaC, LiA, Gedalia B, DelmasY. Shear strengthening effectiveness with CFF strips. Engineering Structures, 2003, 25( 4): 507– 516

[30] MostofinejadD, Tabatabaei KashaniA. Experimental study on effect of EBR and EBROG methods on debonding of FRP sheets used for shear strengthening of RC beams. Composites Part B: Engineering, 2013, 45( 1): 1704– 1713

[31] PandaK C, BhattacharyyaS K, BaraiS V. Effect of transverse steel on the performance of RC T-beams strengthened in shear zone with GFRP sheet. Construction & Building Materials, 2013, 41 : 79– 90

[32] SundarrajaM C, RajamohanS. Strengthening of RC beams in shear using GFRP inclined strips—An experimental study. Construction & Building Materials, 2009, 23( 2): 856– 864

[33] SharkawiA E D M EtmanE. Effect of shear strengthening on the flexural behavior of RC simple beams strengthened externally with FRP laminates. In: Twelfth International Colloquium on Structural and Geotechnical Engineering. Cairo: Ain Shams University, 10– 12

[34] RashidiM TakhtfirouzehH. An experimental study on shear and flexural strengthening of concrete beams using GFRP composites. 2018. arXiv: 1808.10008

[35] NandaR P, BeheraB, MajumderS, KhanH A. RC beam strengthening by glass fibre reinforced polymer. International Journal of Engineering Technology Science and Research, 2018, 5 : 21– 26

[36] DongJ, WangQ, GuanZ. Structural behaviour of RC beams with external flexural and flexural–shear strengthening by FRP sheets. Composites Part B: Engineering, 2013, 44( 1): 604– 612

[37] BaggioD, SoudkiK, NoëlM. Strengthening of shear critical RC beams with various FRP systems. Construction & Building Materials, 2014, 66 : 634– 644

[38] GraceN F, SayedG A, SolimanA K, SalehK R. Strengthening reinforced concrete beams using fiber reinforced polymer (FRP) laminates. ACI Structural Journal—American Concrete Institute, 1999, 96( 5): 865– 874

[39] OzdenS, AtalayH M, AkpinarE, ErdoganH, VulaşY Z. Shear strengthening of reinforced concrete T-beams with fully or partially bonded fibre-reinforced polymer composites. Structural Concrete, 2014, 15( 2): 229– 239

[40] SundarrajaM C, RajamohanS, BhaskarD. Shear strengthening of RC beams using GFRP vertical strips—An experimental study. Journal of Reinforced Plastics and Composites, 2008, 27( 14): 1477– 1495

[41] NandaR P, BeheraB. Experimental study of shear-deficient RC beam wrapped with GFRP. International Journal of Civil Engineering, 2020, 18( 6): 655– 664

[42] Van CaoV, PhamS Q. Comparison of CFRP and GFRP wraps on reducing seismic damage of deficient reinforced concrete structures. International Journal of Civil Engineering, 2019, 17( 11): 1667– 1681

[43] GuadagniniM, PilakoutasK, WaldronP. Shear resistance of FRP RC beams: Experimental study. Journal of Composites for Construction, 2006, 10( 6): 464– 473

[44] SaafanM A A. Shear strengthening of reinforced concrete beams using GFRP wraps. Acta Polytechnica, 2006, 46(1): 24− 32

[45] PanigrahiS K, DebA, Bhattacharyya S K. Modes of failure in shear deficient RC T-beams strengthened with FRP. Journal of Composites for Construction, 2016, 20( 1): 04015029

[46] HawilehR A, RasheedH A, AbdallaJ A, Al-TamimiA K. Behavior of reinforced concrete beams strengthened with externally bonded hybrid fiber reinforced polymer systems. Materials & Design, 2014, 53 : 972– 982

[47] KeskinR S O, ArslanG, SengunK. Influence of CFRP on the shear strength of RC and SFRC beams. Construction & Building Materials, 2017, 153 : 16– 24

[48] TriantafillouT C, AntonopoulosC P. Design of concrete flexural members strengthened in shear with FRP. Journal of Composites for Construction, 2000, 4( 4): 198– 205

[49] TriantafillouT C. Shear strengthening of reinforced concrete beams using epoxy-bonded FRP composites. ACI Structural Journal, 1998, 95 : 107– 115

[50] PellegrinoC, ModenaC. An experimentally based analytical model for the shear capacity of FRP-strengthened reinforced concrete beams. Mechanics of Composite Materials, 2008, 44( 3): 231– 244

[51] PellegrinoC, ModenaC. Fiber reinforced polymer shear strengthening of reinforced concrete beams with transverse steel reinforcement. Journal of Composites for Construction, 2002, 6( 2): 104– 111

[52] PandaK C, BhattacharyyaS K, BaraiS V. Shear strengthening of RC T-beams with externally side bonded GFRP sheet. Journal of Reinforced Plastics and Composites, 2011, 30( 13): 1139– 1154

[53] KhalifaA, NanniA. Rehabilitation of rectangular simply supported RC beams with shear deficiencies using CFRP composites. Construction & Building Materials, 2002, 16( 3): 135– 146

[54] CaoS Y, ChenJ F, TengJ G, HaoZ, Chen J. Debonding in RC beams shear strengthened with complete FRP wraps. Journal of Composites for Construction, 2005, 9( 5): 417– 428

[55] BukhariI A, VollumR L, AhmadS, SagasetaJ. Shear strengthening of reinforced concrete beams with CFRP. Magazine of Concrete Research, 2010, 62( 1): 65– 77

[56] PellegrinoC, ModenaC. Fiber-reinforced polymer shear strengthening of reinforced concrete beams: Experimental study and analytical modeling. ACI Structural Journal, 2006, 103( 5): 720– 728

[57] AdhikaryB B, MutsuyoshiH, AshrafM. Effective shear strengthening of concrete beams using FRP sheets with bonded anchorage. Fibre-Reinforced Polymer Reinforcement for Concrete Structures, 2003, 457– 466

[58] IannirubertoU, ImbimboM. Role of fiber reinforced plastic sheets in shear response of reinforced concrete beams: Experimental and analytical results. Journal of Composites for Construction, 2004, 8( 5): 415– 424

[59] MostofinejadD, Tabatabaei KashaniA, HosseiniA. Design model for shear capacity of RC beams strengthened with two-side CFRP wraps based on effective FRP strain concept. European Journal of Environmental and Civil Engineering, 2016, 20( 2): 161– 179

[60] ChenJ F TengJ G. Shear capacity of FRP-strengthened RC beams: FRP debonding. Construction & Building Materials, 2003, 17(1): 27− 41

[61] ChenJ F TengJ G. Shear capacity of fiber-reinforced polymer-strengthened reinforced concrete beams: Fiber reinforced polymer rupture. Journal of Structural Engineering, 2003, 129(5): 615− 625

[62] KhalifaA, GoldW J, NanniA, MIA A. Contribution of externally bonded FRP to shear capacity of RC flexural members. Journal of Composites for Construction, 1998, 2( 4): 195– 202

[63] MofidiA, ChaallalO. Shear strengthening of RC beams with EB FRP: Influencing factors and conceptual debonding model. Journal of Composites for Construction, 2011, 15( 1): 62– 74

[64] Al-RousanR. Predicting the optimum shear capacity of reinforced concrete beams externally strengthened with CFRP composites. Procedia Manufacturing, 2020, 44 : 631– 638

[65] OzbakkalogluT, LimJ C, VincentT. FRP-confined concrete in circular sections: Review and assessment of stress–strain models. Engineering Structures, 2013, 49 : 1068– 1088

[66] NaserM Z, HawilehR A, AbdallaJ. Modeling strategies of finite element simulation of reinforced concrete beams strengthened with FRP: A review. Journal of Composites Science, 2021, 5( 1): 19– 33

[67] LimaJ L, BarrosJ A. Reliability analysis of shear strengthening externally bonded FRP models. Proceedings of the Institution of Civil Engineers-Structures and Buildings, 2011, 164( 1): 43– 56

[68] PellegrinoC, VasicM. Assessment of design procedures for the use of externally bonded FRP composites in shear strengthening of reinforced concrete beams. Composites Part B: Engineering, 2013, 45( 1): 727– 741

[69] KotyniaR, OllerE, MaríA, KaszubskaM. Efficiency of shear strengthening of RC beams with externally bonded FRP materials—State-of-the-art in the experimental tests. Composite Structures, 2021, 267 : 113891

[70] KangT H K, HowellJ, KimS, Lee D J. A state-of-the-art review on debonding failures of FRP laminates externally adhered to concrete. International Journal of Concrete Structures and Materials, 2012, 6( 2): 123– 134

[71] ShomaliA, MostofinejadD, EsfahaniM R. Effective strain of CFRP in RC beams strengthened in shear with NSM reinforcements. Structures, 2020, 23 : 635– 645

[72] MostofinejadD, ShameliS M. Externally bonded reinforcement in grooves (EBRIG) technique to postpone debonding of FRP sheets in strengthened concrete beams. Construction & Building Materials, 2013, 38 : 751– 758

[73] MostofinejadD, EsfahaniM R, ShomaliA. Experimental and numerical study of the RC beams shear-strengthened with NSM technique. Journal of Composite Materials, 2019, 53( 17): 2377– 2389

[74] HaddadR H, AlmomaniO A. Flexural performance and failure modes of NSM CFRP-strengthened concrete beams: A parametric study. International Journal of Civil Engineering, 2019, 17( 7): 935– 948

[75] BarrosJ A O, DiasS J E, LimaJ L T. Efficacy of CFRP-based techniques for the flexural and shear strengthening of concrete beams. Cement and Concrete Composites, 2007, 29( 3): 203– 217

[76] RizzoA, De LorenzisL. Behavior and capacity of RC beams strengthened in shear with NSM FRP reinforcement. Construction & Building Materials, 2009, 23( 4): 1555– 1567

[77] BarrosJ A O, DiasS J E. Near surface mounted CFRP laminates for shear strengthening of concrete beams. Cement and Concrete Composites, 2006, 28( 3): 276– 292

[78] ShomaliA, MostofinejadD, EsfahaniM R. Shear strengthening of RC beams using EBRIG CFRP strips: A comparative study. European Journal of Environmental and Civil Engineering, 2021, 25( 14): 2540– 2556

[79] BarrosJ DiasS.Shear strengthening of reinforced concrete beams with laminate strips of CFRP. In: Composite in Construction international Conference (CCC2003). Rende: University of Calabria, 2003

[80] ACI440.2R-17. Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures. Farmington Hills, MI: American Concrete Institute, 2017

[81] FIB. Externally bonded FRP reinforcement for RC structures. International Federation for Structural Concrete (fib), 2001, 14 : 138

[82] ArakiN, MatsuzakiY, NakanoK, KatakaT, FukuyamaH. Shear capacity of retrofitted RC members with continuous fibre sheets. Proceedings of 3rd Symposium on Non Metallic (FRP) Reinforcement for Concrete Structures (FRPRCS-3). Tokyo: Japan Concrete Institute, 1997, 515– 522

[83] ZhaoT XieJ. Experimental study on the shear capacity of RC beam strengthened with CFRP sheets. Journal of Building Structures, 2000, 30(7): 21− 25 (in Chinese)

[84] MiyajimaH KosaK TasakiK MatsumotoS. Shear Strengthening of RC Beams Using Carbon Fiber Sheets & Its Resistance Mechanism. Fukuoka: Kyushu Institute of Technology, 2005

[85] UjiK. Improving shear capacity of existing reinforced concrete members by applying carbon fiber sheets. Transactions of the Japan Concrete Institute, 1992, 14 : 253– 266

[86] FunakawaI, ShimonoK, WatanabeT, AsadaS, VshijimaS. Experimental study on shear strengthening with continuous fiber reinforcement sheet and methyl methacrylate resin. In: Proceedings of 3rd Symposium on Non Metallic (FRP) Reinforcement for Concrete Structures (FRPRCS-3). Tokyo: Japan Concrete Institute, 1997, 475– 482

[87] UmezuK, FujitaM, NakaiH, TamakiK. Shear behavior of RC beams with aramid fiber sheet. In: Proceedings of 3rd Symposium on Non Metallic (FRP) Reinforcement for Concrete Structures (FRPRCS-3). Tokyo: Japan Concrete Institute, 1997, 491– 498

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